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Bargaining and membership

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Abstract

In coalitional games in which the players are partitioned into groups, we study the incentives of the members of a group to leave it and become singletons. In this context, we model a non-cooperative mechanism in which each player has to decide whether to stay in her group or to exit and act as a singleton. We show that players, acting myopically, always reach a Nash equilibrium.

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Notes

  1. European People’s Party (Christian Democrats) and European Democrats.

  2. We use the term mechanism instead of non-cooperative game to avoid confusion with coalitional games.

  3. For simplicity, we write {123|45|6} instead of {{1,2,3},{4,5},{6}}, and so on.

  4. We thank María Montero for proposing this example.

  5. We write 146 instead of {1,4,6}, and so on.

  6. A game v is monotonic if v(S)≤v(T) for all S⊆T, and superadditive if v(S)+v(T)≤v(S∪T) for all S,T with S∩T=∅.

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Acknowledgements

A previous version of this paper, titled “Negotiating the membership,” has benefited from helpful comment from Francesc Carreras. Financial support by the Spanish Ministerio de Ciencia e Innovación through grant ECO2011-23460 and the Xunta de Galicia through grant 10PXIB362299PR is gratefully acknowledged.

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Authors and Affiliations

  1. Facultade de CC. Económicas e Empresariais, Universidade de Vigo, Campus Lagoas-Marcosende, s/n, Vigo (Pontevedra), Spain

    María Gómez-Rúa & Juan Vidal-Puga

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  1. María Gómez-Rúa
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  2. Juan Vidal-Puga
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Correspondence to María Gómez-Rúa.

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Gómez-Rúa, M., Vidal-Puga, J. Bargaining and membership. TOP 22, 800–814 (2014). https://doi.org/10.1007/s11750-013-0301-0

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